Stickers, small toys, crayons and lots of snacks are good. Maybe a magazine or two each? If you can find chunky triangular pencils or crayons that won't roll of the tables they make life a lot easier. I would highly recommend bringing a small torch to help you find the bits and pieces that inevitably end up under the seats.
There should be seat-back entertainment screens since it's a long flight. I haven't flown much BA recently, but there are usually short children's TV programmes (lots of CBBC/Nickolodeon/Disney stuff) as well as longer films these days, as well as some simple games to play. But if you have an ipod touch/ipad/portable DVD player it is worth bringing that as a back-up.
When my DCs were little I found it helped get them in the mood for sleep if I changed them into PJs just before boarding or just after take-off. Also taking comfort blankets & one cuddly toy each.
Even if you don't do PJs, take a change of clothes in flight for all of you, in case of spillages, air sickness, toilet accidents or exploding nappies. It's not nice sitting in wet or sick-covered clothes for a long flight, and you are as likely to get covered as they are (toddlers can be very generous with their vomit). Also take zip-loc bags to put anything wet or smelly in, lots of wet-wipes, and more nappies than you think you will need.
You're unlikely to get bulkhead seats unless the flight is empty, as that is where the bassinets are, and yours are too old for them. Also, bulkhead ones may give more space, but the TV screens are on fold-out arms which can get in the way and the folding table/tray things are very good at trapping small fingers.
You probably won't be allowed off first - too many impatient people. When mine were little I always waited till nearly everyone had got off, which made it much easier to get bags sorted and children out of seats, do a final search for lost objects on the floor etc without lots of people huffing and puffing and trying to get past. The flight crew are also more likely to be able to help you after the plane empties out, and you can request assistance in advance if you think you're going to have trouble managing two children and the bags without a buggy.
On some flights if you have handed the buggy in last-minute, at boarding, it will be brought up to the door of the plane or be waiting on the walkway, but sometimes it automatically gets sent to baggage reclaim with everything else - ask if you're not sure.